In an isosceles trapezoid of the base 20 cm and 14 cm, an acute angle of 30 degrees.
| February 1, 2021 | education
In an isosceles trapezoid of the base 20 cm and 14 cm, an acute angle of 30 degrees. find the area of the trapezoid if the side is 10 cm.
1. A, B, C, D – the tops of the trapezoid. Smaller base BC = 14 centimeters. Larger base
AD = 20 centimeters. Side AB = 10 centimeters. ВK – height to the base AD. ∠А = 30 °
2. BK: AB = sine ∠A = sine 30 °.
ВK = AB x 1/2 = 10 x 1/2 = 5 centimeters.
3. Area of the trapezoid = (BC + AD) / 2 x ВK = (14 + 20): 2 x 5 = 17 x 5 = 85 centimeters².
Answer: the area of the trapezoid is 85 centimeters².
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